The frustration-free fully packed loop model

• URL: http://arxiv.org/abs/2206.01758v3
• Date: Fri, 7 Apr 2023 12:26:20 GMT
• Title: The frustration-free fully packed loop model
• Authors: Zhao Zhang and Henrik Schou R{\o}ising
• Abstract summary: We consider a quantum fully packed loop model on the square lattice with a frustration-free projector Hamiltonian and ring-exchange interactions acting on plaquettes. We discuss how the boundary term fractures the Hilbert space into Krylov subspaces, and we prove that the Hamiltonian is ergodic within each subspace. We show that the spectrum is shown to be gapless in the thermodynamic limit with a trial state constructed by adding a twist to the ground state superposition.
• Score: 4.965221313169878
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider a quantum fully packed loop model on the square lattice with a frustration-free projector Hamiltonian and ring-exchange interactions acting on plaquettes. A boundary Hamiltonian is added to favour domain-wall boundary conditions and link ground state properties to the combinatorics and six-vertex model literature. We discuss how the boundary term fractures the Hilbert space into Krylov subspaces, and we prove that the Hamiltonian is ergodic within each subspace, leading to a series of energy-equidistant exact eigenstates in the lower end of the spectrum. Among them we systematically classify both finitely entangled eigenstates and product eigenstates. Using a recursion relation for enumerating half-plane configurations, we compute numerically the exact entanglement entropy of the ground state, confirming area law scaling. Finally, the spectrum is shown to be gapless in the thermodynamic limit with a trial state constructed by adding a twist to the ground state superposition.

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